LMFDB - Embedded newform 216.2.l.b.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(35,216)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("216.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.1
Root			$-0.409484 + 1.35363i$ of defining polynomial
Character	$\chi$	$=$	216.35
Dual form			216.2.l.b.179.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37702 + 0.322193i) q^{2} +(1.79238 - 0.887333i) q^{4} +(-0.565188 - 0.978934i) q^{5} +(-3.71499 - 2.14485i) q^{7} +(-2.18226 + 1.79937i) q^{8} +O(q^{10})$	\(q+(-1.37702 + 0.322193i) q^{2} +(1.79238 - 0.887333i) q^{4} +(-0.565188 - 0.978934i) q^{5} +(-3.71499 - 2.14485i) q^{7} +(-2.18226 + 1.79937i) q^{8} +(1.09368 + 1.16591i) q^{10} +(-1.00953 - 0.582853i) q^{11} +(-2.64466 + 1.52689i) q^{13} +(5.80668 + 1.75656i) q^{14} +(2.42528 - 3.18088i) q^{16} -1.49654i q^{17} -3.42378 q^{19} +(-1.88167 - 1.25312i) q^{20} +(1.57794 + 0.477339i) q^{22} +(-3.85938 - 6.68464i) q^{23} +(1.86113 - 3.22356i) q^{25} +(3.14980 - 2.95466i) q^{26} +(-8.56188 - 0.547960i) q^{28} +(-0.709580 + 1.22903i) q^{29} +(4.66408 - 2.69281i) q^{31} +(-2.31481 + 5.16156i) q^{32} +(0.482173 + 2.06077i) q^{34} +4.84897i q^{35} +2.97201i q^{37} +(4.71462 - 1.10312i) q^{38} +(2.99485 + 1.11931i) q^{40} +(4.23339 - 2.44415i) q^{41} +(-1.74292 + 3.01882i) q^{43} +(-2.32665 - 0.148906i) q^{44} +(7.46820 + 7.96144i) q^{46} +(-1.77991 + 3.08289i) q^{47} +(5.70075 + 9.87399i) q^{49} +(-1.52420 + 5.03856i) q^{50} +(-3.38538 + 5.08347i) q^{52} +11.2786 q^{53} +1.31769i q^{55} +(11.9665 - 2.00402i) q^{56} +(0.581124 - 1.92102i) q^{58} +(-7.50935 + 4.33553i) q^{59} +(3.16057 + 1.82476i) q^{61} +(-5.55494 + 5.21079i) q^{62} +(1.52453 - 7.85340i) q^{64} +(2.98946 + 1.72596i) q^{65} +(-5.58255 - 9.66925i) q^{67} +(-1.32793 - 2.68237i) q^{68} +(-1.56230 - 6.67714i) q^{70} +2.54954 q^{71} -7.06491 q^{73} +(-0.957560 - 4.09253i) q^{74} +(-6.13672 + 3.03803i) q^{76} +(2.50026 + 4.33059i) q^{77} +(2.24998 + 1.29902i) q^{79} +(-4.48461 - 0.576391i) q^{80} +(-5.04198 + 4.72961i) q^{82} +(3.98482 + 2.30064i) q^{83} +(-1.46501 + 0.845824i) q^{85} +(1.42740 - 4.71855i) q^{86} +(3.25183 - 0.544584i) q^{88} -8.63803i q^{89} +13.0998 q^{91} +(-12.8490 - 8.55689i) q^{92} +(1.45769 - 4.81869i) q^{94} +(1.93508 + 3.35165i) q^{95} +(3.35869 - 5.81742i) q^{97} +(-11.0314 - 11.7600i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4	$ 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.37702	+	0.322193i	−0.973702	+	0.227825i
$2$	−1.37702	+	0.322193i	−0.973702	+	0.227825i
$3$		0			0
$3$		0			0
$4$	1.79238	−	0.887333i	0.896192	−	0.443667i
$5$	−0.565188	−	0.978934i	−0.252760	−	0.437793i	0.711525	−	0.702661i	$-0.248005\pi$
$5$	−0.565188	−	0.978934i	−0.252760	−	0.437793i	−0.964285	+	0.264868i	$0.914672\pi$
$6$		0			0
$7$	−3.71499	−	2.14485i	−1.40413	−	0.810677i	−0.409320	−	0.912391i	$-0.634234\pi$
$7$	−3.71499	−	2.14485i	−1.40413	−	0.810677i	−0.994814	+	0.101714i	$0.967567\pi$
$8$	−2.18226	+	1.79937i	−0.771546	+	0.636174i
$9$		0			0
$10$	1.09368	+	1.16591i	0.345853	+	0.368695i
$11$	−1.00953	−	0.582853i	−0.304385	−	0.175737i	0.340026	−	0.940416i	$-0.389564\pi$
$11$	−1.00953	−	0.582853i	−0.304385	−	0.175737i	−0.644411	+	0.764679i	$0.722897\pi$
$12$		0			0
$13$	−2.64466	+	1.52689i	−0.733496	+	0.423484i	−0.819700	−	0.572793i	$-0.805860\pi$
$13$	−2.64466	+	1.52689i	−0.733496	+	0.423484i	0.0862038	+	0.996278i	$0.472526\pi$
$14$	5.80668	+	1.75656i	1.55190	+	0.469461i
$15$		0			0
$16$	2.42528	−	3.18088i	0.606320	−	0.795221i
$17$		−	1.49654i		−	0.362963i	−0.983394	−	0.181482i	$-0.941911\pi$
$17$		−	1.49654i		−	0.362963i	0.983394	−	0.181482i	$-0.0580893\pi$
$18$		0			0
$19$	−3.42378			−0.785468			−0.392734	−	0.919652i	$-0.628471\pi$
$19$	−3.42378			−0.785468			−0.392734	+	0.919652i	$0.628471\pi$
$20$	−1.88167	−	1.25312i	−0.420755	−	0.280205i
$21$		0			0
$22$	1.57794	+	0.477339i	0.336418	+	0.101769i
$23$	−3.85938	−	6.68464i	−0.804736	−	1.39384i	−0.916469	−	0.400106i	$-0.868973\pi$
$23$	−3.85938	−	6.68464i	−0.804736	−	1.39384i	0.111733	−	0.993738i	$-0.464360\pi$
$24$		0			0
$25$	1.86113	−	3.22356i	0.372225	−	0.644713i
$26$	3.14980	−	2.95466i	0.617726	−	0.579456i
$27$		0			0
$28$	−8.56188	−	0.547960i	−1.61804	−	0.103555i
$29$	−0.709580	+	1.22903i	−0.131766	+	0.228225i	−0.924357	−	0.381528i	$-0.875398\pi$
$29$	−0.709580	+	1.22903i	−0.131766	+	0.228225i	0.792592	+	0.609753i	$0.208731\pi$
$30$		0			0
$31$	4.66408	−	2.69281i	0.837694	−	0.483643i	−0.0187859	−	0.999824i	$-0.505980\pi$
$31$	4.66408	−	2.69281i	0.837694	−	0.483643i	0.856480	+	0.516181i	$0.172647\pi$
$32$	−2.31481	+	5.16156i	−0.409204	+	0.912443i
$33$		0			0
$34$	0.482173	+	2.06077i	0.0826920	+	0.353418i
$35$			4.84897i			0.819625i
$36$		0			0
$37$			2.97201i			0.488596i	0.969700	+	0.244298i	$0.0785575\pi$
$37$			2.97201i			0.488596i	−0.969700	+	0.244298i	$0.921443\pi$
$38$	4.71462	−	1.10312i	0.764812	−	0.178949i
$39$		0			0
$40$	2.99485	+	1.11931i	0.473528	+	0.176978i
$41$	4.23339	−	2.44415i	0.661144	−	0.381712i	−0.131569	−	0.991307i	$-0.542001\pi$
$41$	4.23339	−	2.44415i	0.661144	−	0.381712i	0.792713	+	0.609595i	$0.208668\pi$
$42$		0			0
$43$	−1.74292	+	3.01882i	−0.265793	+	0.460366i	−0.967771	−	0.251832i	$-0.918967\pi$
$43$	−1.74292	+	3.01882i	−0.265793	+	0.460366i	0.701978	+	0.712198i	$0.252300\pi$
$44$	−2.32665	−	0.148906i	−0.350756	−	0.0224484i
$45$		0			0
$46$	7.46820	+	7.96144i	1.10113	+	1.17385i
$47$	−1.77991	+	3.08289i	−0.259627	+	0.449686i	−0.966142	−	0.258011i	$-0.916933\pi$
$47$	−1.77991	+	3.08289i	−0.259627	+	0.449686i	0.706515	+	0.707698i	$0.250266\pi$
$48$		0			0
$49$	5.70075	+	9.87399i	0.814393	+	1.41057i
$50$	−1.52420	+	5.03856i	−0.215555	+	0.712560i
$51$		0			0
$52$	−3.38538	+	5.08347i	−0.469467	+	0.704951i
$53$	11.2786			1.54923			0.774616	−	0.632432i	$-0.217943\pi$
$53$	11.2786			1.54923			0.774616	+	0.632432i	$0.217943\pi$
$54$		0			0
$55$			1.31769i			0.177677i
$56$	11.9665	−	2.00402i	1.59908	−	0.267799i
$57$		0			0
$58$	0.581124	−	1.92102i	0.0763053	−	0.252243i
$59$	−7.50935	+	4.33553i	−0.977634	+	0.564437i	−0.901555	−	0.432664i	$-0.857573\pi$
$59$	−7.50935	+	4.33553i	−0.977634	+	0.564437i	−0.0760791	+	0.997102i	$0.524240\pi$
$60$		0			0
$61$	3.16057	+	1.82476i	0.404670	+	0.233636i	0.688497	−	0.725239i	$-0.258271\pi$
$61$	3.16057	+	1.82476i	0.404670	+	0.233636i	−0.283827	+	0.958875i	$0.591604\pi$
$62$	−5.55494	+	5.21079i	−0.705478	+	0.661771i
$63$		0			0
$64$	1.52453	−	7.85340i	0.190566	−	0.981674i
$65$	2.98946	+	1.72596i	0.370796	+	0.214079i
$66$		0			0
$67$	−5.58255	−	9.66925i	−0.682017	−	1.18129i	−0.974364	−	0.224975i	$-0.927770\pi$
$67$	−5.58255	−	9.66925i	−0.682017	−	1.18129i	0.292348	−	0.956312i	$-0.405563\pi$
$68$	−1.32793	−	2.68237i	−0.161035	−	0.325285i
$69$		0			0
$70$	−1.56230	−	6.67714i	−0.186731	−	0.798071i
$71$	2.54954			0.302574			0.151287	−	0.988490i	$-0.451658\pi$
$71$	2.54954			0.302574			0.151287	+	0.988490i	$0.451658\pi$
$72$		0			0
$73$	−7.06491			−0.826885			−0.413442	−	0.910530i	$-0.635674\pi$
$73$	−7.06491			−0.826885			−0.413442	+	0.910530i	$0.635674\pi$
$74$	−0.957560	−	4.09253i	−0.111314	−	0.475747i
$75$		0			0
$76$	−6.13672	+	3.03803i	−0.703930	+	0.348486i
$77$	2.50026	+	4.33059i	0.284932	+	0.493516i
$78$		0			0
$79$	2.24998	+	1.29902i	0.253142	+	0.146152i	0.621202	−	0.783650i	$-0.286645\pi$
$79$	2.24998	+	1.29902i	0.253142	+	0.146152i	−0.368060	+	0.929802i	$0.619978\pi$
$80$	−4.48461	−	0.576391i	−0.501395	−	0.0644424i
$81$		0			0
$82$	−5.04198	+	4.72961i	−0.556794	+	0.522298i
$83$	3.98482	+	2.30064i	0.437391	+	0.252528i	0.702490	−	0.711693i	$-0.252071\pi$
$83$	3.98482	+	2.30064i	0.437391	+	0.252528i	−0.265099	+	0.964221i	$0.585405\pi$
$84$		0			0
$85$	−1.46501	+	0.845824i	−0.158903	+	0.0917425i
$86$	1.42740	−	4.71855i	0.153920	−	0.508814i
$87$		0			0
$88$	3.25183	−	0.544584i	0.346646	−	0.0580529i
$89$		−	8.63803i		−	0.915630i	−0.889048	−	0.457815i	$-0.848632\pi$
$89$		−	8.63803i		−	0.915630i	0.889048	−	0.457815i	$-0.151368\pi$
$90$		0			0
$91$	13.0998			1.37323
$92$	−12.8490	−	8.55689i	−1.33960	−	0.892117i
$93$		0			0
$94$	1.45769	−	4.81869i	0.150349	−	0.497010i
$95$	1.93508	+	3.35165i	0.198535	+	0.343872i
$96$		0			0
$97$	3.35869	−	5.81742i	0.341023	−	0.590670i	−0.643600	−	0.765362i	$-0.722560\pi$
$97$	3.35869	−	5.81742i	0.341023	−	0.590670i	0.984623	+	0.174693i	$0.0558931\pi$
$98$	−11.0314	−	11.7600i	−1.11434	−	1.18794i
$99$		0			0
$100$	0.475475	−	7.42930i	0.0475475	−	0.742930i
$101$	−6.86479	+	11.8902i	−0.683072	+	1.18312i	0.290967	+	0.956733i	$0.406023\pi$
$101$	−6.86479	+	11.8902i	−0.683072	+	1.18312i	−0.974039	+	0.226382i	$0.927310\pi$
$102$		0			0
$103$	5.48137	−	3.16467i	0.540095	−	0.311824i	−0.205022	−	0.978757i	$-0.565727\pi$
$103$	5.48137	−	3.16467i	0.540095	−	0.311824i	0.745118	+	0.666933i	$0.232393\pi$
$104$	3.02388	−	8.09080i	0.296516	−	0.793368i
$105$		0			0
$106$	−15.5309	+	3.63388i	−1.50849	+	0.352953i
$107$		−	10.4483i		−	1.01007i	−0.863097	−	0.505037i	$-0.831479\pi$
$107$		−	10.4483i		−	1.01007i	0.863097	−	0.505037i	$-0.168521\pi$
$108$		0			0
$109$		−	9.67531i		−	0.926727i	−0.886168	−	0.463364i	$-0.846642\pi$
$109$		−	9.67531i		−	0.926727i	0.886168	−	0.463364i	$-0.153358\pi$
$110$	−0.424549	−	1.81448i	−0.0404792	−	0.173004i
$111$		0			0
$112$	−15.8324	+	6.61509i	−1.49602	+	0.625067i
$113$	−7.15149	+	4.12891i	−0.672756	+	0.388416i	−0.797120	−	0.603821i	$-0.793644\pi$
$113$	−7.15149	+	4.12891i	−0.672756	+	0.388416i	0.124364	+	0.992237i	$0.460311\pi$
$114$		0			0
$115$	−4.36255	+	7.55615i	−0.406810	+	0.704615i
$116$	−0.181281	+	2.83253i	−0.0168316	+	0.262993i
$117$		0			0
$118$	8.94367	−	8.38958i	0.823332	−	0.772323i
$119$	−3.20984	+	5.55961i	−0.294246	+	0.509649i
$120$		0			0
$121$	−4.82056	−	8.34946i	−0.438233	−	0.759042i
$122$	−4.94011	−	1.49442i	−0.447256	−	0.135298i
$123$		0			0
$124$	5.97040	−	8.96514i	0.536158	−	0.805093i
$125$	−9.85942			−0.881853
$126$		0			0
$127$			2.78757i			0.247357i	0.992322	+	0.123678i	$0.0394691\pi$
$127$			2.78757i			0.247357i	−0.992322	+	0.123678i	$0.960531\pi$
$128$	0.431001	+	11.3055i	0.0380955	+	0.999274i
$129$		0			0
$130$	−4.67264	−	1.41351i	−0.409818	−	0.123973i
$131$	13.0529	−	7.53612i	1.14044	−	0.658434i	0.193901	−	0.981021i	$-0.437886\pi$
$131$	13.0529	−	7.53612i	1.14044	−	0.658434i	0.946540	+	0.322587i	$0.104553\pi$
$132$		0			0
$133$	12.7193	+	7.34348i	1.10290	+	0.636761i
$134$	10.8027	+	11.5161i	0.933207	+	0.994842i
$135$		0			0
$136$	2.69283	+	3.26583i	0.230908	+	0.280043i
$137$	−7.55211	−	4.36021i	−0.645220	−	0.372518i	0.141402	−	0.989952i	$-0.454839\pi$
$137$	−7.55211	−	4.36021i	−0.645220	−	0.372518i	−0.786623	+	0.617434i	$0.788172\pi$
$138$		0			0
$139$	1.18897	+	2.05935i	0.100847	+	0.174672i	0.912034	−	0.410115i	$-0.134511\pi$
$139$	1.18897	+	2.05935i	0.100847	+	0.174672i	−0.811187	+	0.584787i	$0.801178\pi$
$140$	4.30265	+	8.69121i	0.363641	+	0.734542i
$141$		0			0
$142$	−3.51077	+	0.821442i	−0.294617	+	0.0689339i
$143$	3.55982			0.297687
$144$		0			0
$145$	1.60418			0.133220
$146$	9.72854	−	2.27626i	0.805139	−	0.188385i
$147$		0			0
$148$	2.63717	+	5.32698i	0.216774	+	0.437875i
$149$	−8.94426	−	15.4919i	−0.732742	−	1.26915i	−0.955707	−	0.294320i	$-0.904907\pi$
$149$	−8.94426	−	15.4919i	−0.732742	−	1.26915i	0.222965	−	0.974826i	$-0.428426\pi$
$150$		0			0
$151$	−2.39162	−	1.38080i	−0.194627	−	0.112368i	0.399520	−	0.916725i	$-0.369177\pi$
$151$	−2.39162	−	1.38080i	−0.194627	−	0.112368i	−0.594147	+	0.804357i	$0.702510\pi$
$152$	7.47158	−	6.16065i	0.606025	−	0.499694i
$153$		0			0
$154$	−4.83820	−	5.15775i	−0.389874	−	0.415623i
$155$	−5.27216	−	3.04388i	−0.423470	−	0.244491i
$156$		0			0
$157$	−2.21148	+	1.27680i	−0.176495	+	0.101900i	−0.585645	−	0.810568i	$-0.699159\pi$
$157$	−2.21148	+	1.27680i	−0.176495	+	0.101900i	0.409150	+	0.912467i	$0.365825\pi$
$158$	−3.51681	−	1.06386i	−0.279782	−	0.0846362i
$159$		0			0
$160$	6.36112	−	0.651206i	0.502891	−	0.0514824i
$161$			33.1111i			2.60952i
$162$		0			0
$163$	6.93355			0.543077			0.271539	−	0.962428i	$-0.412468\pi$
$163$	6.93355			0.543077			0.271539	+	0.962428i	$0.412468\pi$
$164$	5.41908	−	8.13728i	0.423159	−	0.635414i
$165$		0			0
$166$	−6.22844	−	1.88415i	−0.483421	−	0.146239i
$167$	8.36829	+	14.4943i	0.647558	+	1.12160i	0.983704	+	0.179794i	$0.0575430\pi$
$167$	8.36829	+	14.4943i	0.647558	+	1.12160i	−0.336146	+	0.941810i	$0.609124\pi$
$168$		0			0
$169$	−1.83719	+	3.18211i	−0.141322	+	0.244778i
$170$	1.74483	−	1.63673i	0.133823	−	0.125532i
$171$		0			0
$172$	−0.445276	+	6.95744i	−0.0339520	+	0.530500i
$173$	10.2190	−	17.6999i	0.776938	−	1.34570i	−0.156761	−	0.987637i	$-0.550105\pi$
$173$	10.2190	−	17.6999i	0.776938	−	1.34570i	0.933699	−	0.358059i	$-0.116562\pi$
$174$		0			0
$175$	−13.8281	+	7.98367i	−1.04531	+	0.603508i
$176$	−4.30238	+	1.79762i	−0.324304	+	0.135501i
$177$		0			0
$178$	2.78311	+	11.8948i	0.208603	+	0.891550i
$179$			4.07982i			0.304940i	0.988308	+	0.152470i	$0.0487227\pi$
$179$			4.07982i			0.304940i	−0.988308	+	0.152470i	$0.951277\pi$
$180$		0			0
$181$		−	22.3226i		−	1.65923i	−0.558337	−	0.829614i	$-0.688560\pi$
$181$		−	22.3226i		−	1.65923i	0.558337	−	0.829614i	$-0.311440\pi$
$182$	−18.0388	+	4.22067i	−1.33712	+	0.312857i
$183$		0			0
$184$	20.4503	+	7.64317i	1.50762	+	0.563462i
$185$	2.90940	−	1.67974i	0.213904	−	0.123497i
$186$		0			0
$187$	−0.872261	+	1.51080i	−0.0637861	+	0.110481i
$188$	−0.454726	+	7.10510i	−0.0331643	+	0.518193i
$189$		0			0
$190$	−3.74452	−	3.99183i	−0.271656	−	0.289598i
$191$	7.27481	−	12.6003i	0.526387	−	0.911728i	−0.473141	−	0.880987i	$-0.656880\pi$
$191$	7.27481	−	12.6003i	0.526387	−	0.911728i	0.999527	−	0.0307415i	$-0.00978686\pi$
$192$		0			0
$193$	2.19526	+	3.80230i	0.158018	+	0.273696i	0.934154	−	0.356870i	$-0.116156\pi$
$193$	2.19526	+	3.80230i	0.158018	+	0.273696i	−0.776136	+	0.630566i	$0.782823\pi$
$194$	−2.75066	+	9.09287i	−0.197486	+	0.652830i
$195$		0			0
$196$	18.9795	+	12.6395i	1.35568	+	0.902823i
$197$	−7.69721			−0.548404			−0.274202	−	0.961672i	$-0.588414\pi$
$197$	−7.69721			−0.548404			−0.274202	+	0.961672i	$0.588414\pi$
$198$		0			0
$199$			20.9790i			1.48716i	0.668646	+	0.743580i	$0.266874\pi$
$199$			20.9790i			1.48716i	−0.668646	+	0.743580i	$0.733126\pi$
$200$	1.73893	+	10.3835i	0.122961	+	0.734225i
$201$		0			0
$202$	5.62204	−	18.5848i	0.395566	−	1.30762i
$203$	5.27216	−	3.04388i	0.370033	−	0.213639i
$204$		0			0
$205$	−4.78532	−	2.76280i	−0.334221	−	0.192963i
$206$	−6.52834	+	6.12388i	−0.454851	+	0.426671i
$207$		0			0
$208$	−1.55716	+	12.1155i	−0.107970	+	0.840058i
$209$	3.45641	+	1.99556i	0.239085	+	0.138036i
$210$		0			0
$211$	2.38482	+	4.13063i	0.164178	+	0.284364i	0.936363	−	0.351033i	$-0.114170\pi$
$211$	2.38482	+	4.13063i	0.164178	+	0.284364i	−0.772185	+	0.635397i	$0.780836\pi$
$212$	20.2155	−	10.0079i	1.38841	−	0.687343i
$213$		0			0
$214$	3.36636	+	14.3875i	0.230120	+	0.983512i
$215$	3.94031			0.268727
$216$		0			0
$217$	−23.1027			−1.56831
$218$	3.11732	+	13.3231i	0.211131	+	0.902356i
$219$		0			0
$220$	1.16923	+	2.36180i	0.0788293	+	0.159232i
$221$	2.28505	+	3.95783i	0.153709	+	0.266232i
$222$		0			0
$223$	−12.5272	−	7.23260i	−0.838886	−	0.484331i	0.0179997	−	0.999838i	$-0.494270\pi$
$223$	−12.5272	−	7.23260i	−0.838886	−	0.484331i	−0.856885	+	0.515507i	$0.827604\pi$
$224$	19.6702	−	14.2102i	1.31427	−	0.949459i
$225$		0			0
$226$	8.51746	−	7.98977i	0.566573	−	0.531471i
$227$	−0.561821	−	0.324367i	−0.0372894	−	0.0215290i	0.481239	−	0.876589i	$-0.340187\pi$
$227$	−0.561821	−	0.324367i	−0.0372894	−	0.0215290i	−0.518529	+	0.855060i	$0.673520\pi$
$228$		0			0
$229$	−12.0007	+	6.92863i	−0.793032	+	0.457857i	−0.841029	−	0.540990i	$-0.818050\pi$
$229$	−12.0007	+	6.92863i	−0.793032	+	0.457857i	0.0479971	+	0.998847i	$0.484716\pi$
$230$	3.57279	−	11.8106i	0.235583	−	0.778767i
$231$		0			0
$232$	−0.662990	−	3.95886i	−0.0435275	−	0.259912i
$233$		−	23.1276i		−	1.51514i	−0.652755	−	0.757569i	$-0.726387\pi$
$233$		−	23.1276i		−	1.51514i	0.652755	−	0.757569i	$-0.273613\pi$
$234$		0			0
$235$	4.02393			0.262492
$236$	−9.61258	+	14.4342i	−0.625726	+	0.939588i
$237$		0			0
$238$	2.62876	−	8.68990i	0.170397	−	0.563283i
$239$	−7.44075	−	12.8878i	−0.481302	−	0.833640i	0.518468	−	0.855097i	$-0.326503\pi$
$239$	−7.44075	−	12.8878i	−0.481302	−	0.833640i	−0.999770	+	0.0214576i	$0.993169\pi$
$240$		0			0
$241$	−5.87960	+	10.1838i	−0.378738	+	0.655994i	−0.990879	−	0.134755i	$-0.956975\pi$
$241$	−5.87960	+	10.1838i	−0.378738	+	0.655994i	0.612141	+	0.790749i	$0.290309\pi$
$242$	9.32816	+	9.94425i	0.599637	+	0.639241i
$243$		0			0
$244$	7.28413	+	0.466184i	0.466319	+	0.0298444i
$245$	6.44399	−	11.1613i	0.411691	−	0.713071i
$246$		0			0
$247$	9.05472	−	5.22774i	0.576138	−	0.332633i
$248$	−5.33288	+	14.2688i	−0.338638	+	0.906071i
$249$		0			0
$250$	13.5766	−	3.17663i	0.858662	−	0.200908i
$251$		−	5.51619i		−	0.348179i	−0.984730	−	0.174089i	$-0.944302\pi$
$251$		−	5.51619i		−	0.348179i	0.984730	−	0.174089i	$-0.0556981\pi$
$252$		0			0
$253$			8.99781i			0.565687i
$254$	−0.898134	−	3.83854i	−0.0563539	−	0.240852i
$255$		0			0
$256$	−4.23605	−	15.4291i	−0.264753	−	0.964316i
$257$	−16.9194	+	9.76841i	−1.05540	+	0.609337i	−0.924157	−	0.382013i	$-0.875231\pi$
$257$	−16.9194	+	9.76841i	−1.05540	+	0.609337i	−0.131245	+	0.991350i	$0.541898\pi$
$258$		0			0
$259$	6.37451	−	11.0410i	0.396093	−	0.686053i
$260$	6.88976	+	0.440944i	0.427285	+	0.0273462i
$261$		0			0
$262$	−15.5461	+	14.5830i	−0.960442	+	0.900939i
$263$	5.62576	−	9.74411i	0.346899	−	0.600847i	−0.638798	−	0.769375i	$-0.720568\pi$
$263$	5.62576	−	9.74411i	0.346899	−	0.600847i	0.985697	+	0.168527i	$0.0539012\pi$
$264$		0			0
$265$	−6.37451	−	11.0410i	−0.391583	−	0.678242i
$266$	−19.8808	−	6.01408i	−1.21897	−	0.368747i
$267$		0			0
$268$	−18.5859	−	12.3774i	−1.13532	−	0.756072i
$269$	−14.1600			−0.863350			−0.431675	−	0.902029i	$-0.642077\pi$
$269$	−14.1600			−0.863350			−0.431675	+	0.902029i	$0.642077\pi$
$270$		0			0
$271$		−	3.91574i		−	0.237864i	−0.992902	−	0.118932i	$-0.962053\pi$
$271$		−	3.91574i		−	0.237864i	0.992902	−	0.118932i	$-0.0379471\pi$
$272$	−4.76031	−	3.62952i	−0.288636	−	0.220072i
$273$		0			0
$274$	11.8043	+	3.57088i	0.713121	+	0.215725i
$275$	−3.75773	+	2.16953i	−0.226600	+	0.130827i
$276$		0			0
$277$	−22.9537	−	13.2523i	−1.37915	−	0.796253i	−0.387094	−	0.922040i	$-0.626521\pi$
$277$	−22.9537	−	13.2523i	−1.37915	−	0.796253i	−0.992057	+	0.125787i	$0.959854\pi$
$278$	−2.30074	−	2.45270i	−0.137989	−	0.147103i
$279$		0			0
$280$	−8.72510	−	10.5817i	−0.521424	−	0.632378i
$281$	0.923368	+	0.533106i	0.0550835	+	0.0318025i	0.527289	−	0.849686i	$-0.323209\pi$
$281$	0.923368	+	0.533106i	0.0550835	+	0.0318025i	−0.472205	+	0.881489i	$0.656542\pi$
$282$		0			0
$283$	1.77840	+	3.08028i	0.105715	+	0.183103i	0.914030	−	0.405647i	$-0.132954\pi$
$283$	1.77840	+	3.08028i	0.105715	+	0.183103i	−0.808315	+	0.588750i	$0.799620\pi$
$284$	4.56975	−	2.26229i	0.271165	−	0.134242i
$285$		0			0
$286$	−4.90195	+	1.14695i	−0.289859	+	0.0678205i
$287$	−20.9693			−1.23778
$288$		0			0
$289$	14.7604			0.868258
$290$	−2.20900	+	0.516856i	−0.129717	+	0.0303509i
$291$		0			0
$292$	−12.6630	+	6.26893i	−0.741047	+	0.366861i
$293$	7.78958	+	13.4919i	0.455072	+	0.788208i	0.998692	−	0.0511233i	$-0.0162802\pi$
$293$	7.78958	+	13.4919i	0.455072	+	0.788208i	−0.543620	+	0.839331i	$0.682947\pi$
$294$		0			0
$295$	8.48839	+	4.90077i	0.494213	+	0.285334i
$296$	−5.34775	−	6.48570i	−0.310832	−	0.376974i
$297$		0			0
$298$	17.3078	+	18.4509i	1.00262	+	1.06883i
$299$	20.4135	+	11.7857i	1.18054	+	0.681586i
$300$		0			0
$301$	12.9498	−	7.47659i	0.746416	−	0.430944i
$302$	3.73819	+	1.13083i	0.215109	+	0.0650721i
$303$		0			0
$304$	−8.30361	+	10.8906i	−0.476245	+	0.624621i
$305$		−	4.12532i		−	0.236215i
$306$		0			0
$307$	−0.960690			−0.0548295			−0.0274147	−	0.999624i	$-0.508727\pi$
$307$	−0.960690			−0.0548295			−0.0274147	+	0.999624i	$0.508727\pi$
$308$	8.32411	+	5.54350i	0.474310	+	0.315870i
$309$		0			0
$310$	8.24061	+	2.49285i	0.468035	+	0.141584i
$311$	4.49539	+	7.78624i	0.254910	+	0.441517i	0.964871	−	0.262724i	$-0.0846208\pi$
$311$	4.49539	+	7.78624i	0.254910	+	0.441517i	−0.709961	+	0.704241i	$0.751287\pi$
$312$		0			0
$313$	8.55885	−	14.8244i	0.483775	−	0.837923i	−0.516051	−	0.856558i	$-0.672599\pi$
$313$	8.55885	−	14.8244i	0.483775	−	0.837923i	0.999826	+	0.0186349i	$0.00593201\pi$
$314$	2.63388	−	2.47070i	0.148639	−	0.139430i
$315$		0			0
$316$	5.18549	+	0.331871i	0.291707	+	0.0186692i
$317$	−3.96528	+	6.86806i	−0.222712	+	0.385749i	−0.955631	−	0.294568i	$-0.904824\pi$
$317$	−3.96528	+	6.86806i	−0.222712	+	0.385749i	0.732919	+	0.680316i	$0.238158\pi$
$318$		0			0
$319$	1.43269	−	0.827162i	0.0802151	−	0.0463122i
$320$	−8.54960	+	2.94623i	−0.477937	+	0.164699i
$321$		0			0
$322$	−10.6682	−	45.5948i	−0.594514	−	2.54090i
$323$			5.12381i			0.285096i
$324$		0			0
$325$			11.3670i			0.630526i
$326$	−9.54765	+	2.23394i	−0.528796	+	0.123726i
$327$		0			0
$328$	−4.84043	+	12.9512i	−0.267268	+	0.715111i
$329$	13.2247	−	7.63528i	0.729101	−	0.420946i
$330$		0			0
$331$	4.78348	−	8.28523i	0.262924	−	0.455397i	−0.704094	−	0.710107i	$-0.748647\pi$
$331$	4.78348	−	8.28523i	0.262924	−	0.455397i	0.967018	+	0.254710i	$0.0819799\pi$
$332$	9.18377	+	0.587761i	0.504025	+	0.0322576i
$333$		0			0
$334$	−16.1933	−	17.2628i	−0.886058	−	0.944578i
$335$	−6.31037	+	10.9299i	−0.344773	+	0.597164i
$336$		0			0
$337$	17.0727	+	29.5707i	0.930007	+	1.61082i	0.783305	+	0.621638i	$0.213532\pi$
$337$	17.0727	+	29.5707i	0.930007	+	1.61082i	0.146702	+	0.989181i	$0.453134\pi$
$338$	1.50460	−	4.97377i	0.0818396	−	0.270537i
$339$		0			0
$340$	−1.87533	+	2.81599i	−0.101704	+	0.152719i
$341$	−6.27805			−0.339975
$342$		0			0
$343$		−	18.8811i		−	1.01949i
$344$	−1.62848	−	9.72402i	−0.0878019	−	0.524284i
$345$		0			0
$346$	−8.36906	+	27.6656i	−0.449923	+	1.48731i
$347$	−20.9431	+	12.0915i	−1.12428	+	0.649105i	−0.942491	−	0.334232i	$-0.891523\pi$
$347$	−20.9431	+	12.0915i	−1.12428	+	0.649105i	−0.181792	+	0.983337i	$0.558190\pi$
$348$		0			0
$349$	9.71845	+	5.61095i	0.520217	+	0.300347i	0.737023	−	0.675867i	$-0.236231\pi$
$349$	9.71845	+	5.61095i	0.520217	+	0.300347i	−0.216807	+	0.976215i	$0.569564\pi$
$350$	16.4694	−	15.4490i	0.880324	−	0.825784i
$351$		0			0
$352$	5.34530	−	3.86156i	0.284906	−	0.205822i
$353$	5.85176	+	3.37852i	0.311458	+	0.179820i	0.647579	−	0.761999i	$-0.275782\pi$
$353$	5.85176	+	3.37852i	0.311458	+	0.179820i	−0.336121	+	0.941819i	$0.609115\pi$
$354$		0			0
$355$	−1.44097	−	2.49583i	−0.0764786	−	0.132465i
$356$	−7.66481	−	15.4827i	−0.406234	−	0.820580i
$357$		0			0
$358$	−1.31449	−	5.61800i	−0.0694728	−	0.296921i
$359$	−20.3395			−1.07348			−0.536739	−	0.843748i	$-0.680344\pi$
$359$	−20.3395			−1.07348			−0.536739	+	0.843748i	$0.680344\pi$
$360$		0			0
$361$	−7.27775			−0.383039
$362$	7.19219	+	30.7388i	0.378013	+	1.61559i
$363$		0			0
$364$	23.4799	−	11.6239i	1.23068	−	0.609259i
$365$	3.99300	+	6.91608i	0.209003	+	0.362004i
$366$		0			0
$367$	11.7198	+	6.76642i	0.611767	+	0.353204i	0.773657	−	0.633605i	$-0.218425\pi$
$367$	11.7198	+	6.76642i	0.611767	+	0.353204i	−0.161889	+	0.986809i	$0.551759\pi$
$368$	−30.6231	−	3.93588i	−1.59634	−	0.205172i
$369$		0			0
$370$	−3.46511	+	3.25043i	−0.180143	+	0.168982i
$371$	−41.8998	−	24.1908i	−2.17533	−	1.25593i
$372$		0			0
$373$	23.0364	−	13.3001i	1.19278	−	0.688651i	0.233843	−	0.972274i	$-0.424870\pi$
$373$	23.0364	−	13.3001i	1.19278	−	0.688651i	0.958936	+	0.283623i	$0.0915364\pi$
$374$	0.714355	−	2.36144i	0.0369384	−	0.122107i
$375$		0			0
$376$	−1.66304	−	9.93040i	−0.0857650	−	0.512121i
$377$		−	4.33381i		−	0.223203i
$378$		0			0
$379$	−28.5030			−1.46410			−0.732050	−	0.681251i	$-0.761436\pi$
$379$	−28.5030			−1.46410			−0.732050	+	0.681251i	$0.761436\pi$
$380$	6.44243	+	4.29039i	0.330490	+	0.220092i
$381$		0			0
$382$	−5.95784	+	19.6948i	−0.304830	+	1.00768i
$383$	10.0515	+	17.4097i	0.513606	+	0.889592i	0.999875	+	0.0157832i	$0.00502416\pi$
$383$	10.0515	+	17.4097i	0.513606	+	0.889592i	−0.486269	+	0.873809i	$0.661643\pi$
$384$		0			0
$385$	2.82624	−	4.89519i	0.144038	−	0.249482i
$386$	−4.24800	−	4.52856i	−0.216217	−	0.230498i
$387$		0			0
$388$	0.858068	−	13.4073i	0.0435618	−	0.680654i
$389$	1.08110	−	1.87253i	0.0548142	−	0.0949409i	−0.837316	−	0.546719i	$-0.815877\pi$
$389$	1.08110	−	1.87253i	0.0548142	−	0.0949409i	0.892130	+	0.451778i	$0.149210\pi$
$390$		0			0
$391$	−10.0038	+	5.77570i	−0.505914	+	0.292090i
$392$	−30.2075	−	11.2899i	−1.52571	−	0.570224i
$393$		0			0
$394$	10.5992	−	2.47999i	0.533982	−	0.124940i
$395$		−	2.93677i		−	0.147765i
$396$		0			0
$397$			18.8504i			0.946076i	0.881042	+	0.473038i	$0.156843\pi$
$397$			18.8504i			0.946076i	−0.881042	+	0.473038i	$0.843157\pi$
$398$	−6.75928	−	28.8885i	−0.338812	−	1.44805i
$399$		0			0
$400$	−5.74004	−	13.7381i	−0.287002	−	0.686903i
$401$	15.0668	−	8.69883i	0.752401	−	0.434399i	−0.0741601	−	0.997246i	$-0.523628\pi$
$401$	15.0668	−	8.69883i	0.752401	−	0.434399i	0.826561	+	0.562848i	$0.190294\pi$
$402$		0			0
$403$	−8.22326	+	14.2431i	−0.409630	+	0.709500i
$404$	−1.75380	+	27.4031i	−0.0872546	+	1.36335i
$405$		0			0
$406$	−6.27917	+	5.89015i	−0.311630	+	0.292323i
$407$	1.73225	−	3.00034i	0.0858643	−	0.148721i
$408$		0			0
$409$	−10.2872	−	17.8179i	−0.508667	−	0.881037i	−0.999950	−	0.0100370i	$-0.996805\pi$
$409$	−10.2872	−	17.8179i	−0.508667	−	0.881037i	0.491282	−	0.871000i	$-0.336528\pi$
$410$	7.47965	+	2.26265i	0.369393	+	0.111744i
$411$		0			0
$412$	7.01660	−	10.5361i	0.345683	−	0.519077i
$413$	37.1962			1.83030
$414$		0			0
$415$		−	5.20117i		−	0.255316i
$416$	−1.75928	−	17.1850i	−0.0862557	−	0.842565i
$417$		0			0
$418$	−5.40251	−	1.63430i	−0.264246	−	0.0799363i
$419$	24.1959	−	13.9695i	1.18205	−	0.682455i	0.225560	−	0.974229i	$-0.427579\pi$
$419$	24.1959	−	13.9695i	1.18205	−	0.682455i	0.956487	+	0.291774i	$0.0942454\pi$
$420$		0			0
$421$	6.27826	+	3.62475i	0.305983	+	0.176660i	0.645128	−	0.764075i	$-0.276804\pi$
$421$	6.27826	+	3.62475i	0.305983	+	0.176660i	−0.339144	+	0.940734i	$0.610137\pi$
$422$	−4.61481	−	4.91960i	−0.224645	−	0.239482i
$423$		0			0
$424$	−24.6128	+	20.2944i	−1.19530	+	0.985581i
$425$	−4.82418	−	2.78524i	−0.234007	−	0.135104i
$426$		0			0
$427$	−7.82766	−	13.5579i	−0.378807	−	0.656113i
$428$	−9.27112	−	18.7274i	−0.448137	−	0.905221i
$429$		0			0
$430$	−5.42589	+	1.26954i	−0.261660	+	0.0612225i
$431$	37.7004			1.81596			0.907982	−	0.419009i	$-0.137623\pi$
$431$	37.7004			1.81596			0.907982	+	0.419009i	$0.137623\pi$
$432$		0			0
$433$	36.1185			1.73575			0.867873	−	0.496787i	$-0.165487\pi$
$433$	36.1185			1.73575			0.867873	+	0.496787i	$0.165487\pi$
$434$	31.8129	−	7.44351i	1.52707	−	0.357300i
$435$		0			0
$436$	−8.58523	−	17.3419i	−0.411158	−	0.830525i
$437$	13.2137	+	22.8867i	0.632095	+	1.09482i
$438$		0			0
$439$	−9.02239	−	5.20908i	−0.430615	−	0.248616i	0.268993	−	0.963142i	$-0.413309\pi$
$439$	−9.02239	−	5.20908i	−0.430615	−	0.248616i	−0.699609	+	0.714526i	$0.746642\pi$
$440$	−2.37101	−	2.87554i	−0.113033	−	0.137086i
$441$		0			0
$442$	−4.42175	−	4.71379i	−0.210321	−	0.224212i
$443$	30.7905	+	17.7769i	1.46290	+	0.844606i	0.999144	−	0.0413574i	$-0.0131682\pi$
$443$	30.7905	+	17.7769i	1.46290	+	0.844606i	0.463756	+	0.885963i	$0.346502\pi$
$444$		0			0
$445$	−8.45606	+	4.88211i	−0.400856	+	0.231434i
$446$	19.5806	+	5.92327i	0.927167	+	0.280475i
$447$		0			0
$448$	−22.5079	+	25.9054i	−1.06340	+	1.22391i
$449$			16.7750i			0.791662i	0.918323	+	0.395831i	$0.129543\pi$
$449$			16.7750i			0.791662i	−0.918323	+	0.395831i	$0.870457\pi$
$450$		0			0
$451$	−5.69832			−0.268323
$452$	−9.15449	+	13.7464i	−0.430591	+	0.646574i
$453$		0			0
$454$	0.878149	+	0.265647i	0.0412136	+	0.0124674i
$455$	−7.40386	−	12.8239i	−0.347098	−	0.601192i
$456$		0			0
$457$	−0.679436	+	1.17682i	−0.0317827	+	0.0550492i	−0.881479	−	0.472223i	$-0.843452\pi$
$457$	−0.679436	+	1.17682i	−0.0317827	+	0.0550492i	0.849697	+	0.527272i	$0.176785\pi$
$458$	14.2929	−	13.4074i	0.667866	−	0.626489i
$459$		0			0
$460$	−1.11453	+	17.4146i	−0.0519653	+	0.811958i
$461$	−5.07410	+	8.78860i	−0.236324	+	0.409326i	−0.959657	−	0.281174i	$-0.909276\pi$
$461$	−5.07410	+	8.78860i	−0.236324	+	0.409326i	0.723332	+	0.690500i	$0.242609\pi$
$462$		0			0
$463$	23.2656	−	13.4324i	1.08124	−	0.624256i	0.150012	−	0.988684i	$-0.452069\pi$
$463$	23.2656	−	13.4324i	1.08124	−	0.624256i	0.931232	+	0.364428i	$0.118735\pi$
$464$	2.18847	+	5.23783i	0.101597	+	0.243160i
$465$		0			0
$466$	7.45153	+	31.8472i	0.345186	+	1.47529i
$467$			31.4118i			1.45356i	0.686868	+	0.726782i	$0.258985\pi$
$467$			31.4118i			1.45356i	−0.686868	+	0.726782i	$0.741015\pi$
$468$		0			0
$469$			47.8949i			2.21158i
$470$	−5.54105	+	1.29648i	−0.255590	+	0.0598023i
$471$		0			0
$472$	8.58614	−	22.9734i	0.395209	−	1.05743i
$473$	3.51906	−	2.03173i	0.161807	−	0.0934191i
$474$		0			0
$475$	−6.37208	+	11.0368i	−0.292371	+	0.506402i
$476$	−0.820042	+	12.8132i	−0.0375866	+	0.587290i
$477$		0			0
$478$	14.3984	+	15.3494i	0.658568	+	0.702064i
$479$	2.42488	−	4.20001i	0.110796	−	0.191904i	−0.805296	−	0.592873i	$-0.797993\pi$
$479$	2.42488	−	4.20001i	0.110796	−	0.191904i	0.916091	+	0.400970i	$0.131327\pi$
$480$		0			0
$481$	−4.53794	−	7.85995i	−0.206912	−	0.358383i
$482$	4.81521	−	15.9176i	0.219327	−	0.725028i
$483$		0			0
$484$	−16.0491	−	10.6880i	−0.729503	−	0.485818i
$485$	−7.59316			−0.344788
$486$		0			0
$487$		−	23.2664i		−	1.05430i	−0.849772	−	0.527150i	$-0.823261\pi$
$487$		−	23.2664i		−	1.05430i	0.849772	−	0.527150i	$-0.176739\pi$
$488$	−10.1806	+	1.70495i	−0.460855	+	0.0771794i
$489$		0			0
$490$	−5.27743	+	17.4456i	−0.238410	+	0.788112i
$491$	−9.48139	+	5.47408i	−0.427889	+	0.247042i	−0.698447	−	0.715662i	$-0.746125\pi$
$491$	−9.48139	+	5.47408i	−0.427889	+	0.247042i	0.270558	+	0.962704i	$0.412792\pi$
$492$		0			0
$493$	1.83929	+	1.06191i	0.0828373	+	0.0478262i
$494$	−10.7842	+	10.1161i	−0.485205	+	0.455144i
$495$		0			0
$496$	2.74618	−	21.3667i	0.123307	−	0.959394i
$497$	−9.47149	−	5.46837i	−0.424855	−	0.245290i
$498$		0			0
$499$	19.4409	+	33.6726i	0.870293	+	1.50739i	0.861694	+	0.507429i	$0.169404\pi$
$499$	19.4409	+	33.6726i	0.870293	+	1.50739i	0.00859924	+	0.999963i	$0.497263\pi$
$500$	−17.6719	+	8.74859i	−0.790310	+	0.391249i
$501$		0			0
$502$	1.77727	+	7.59591i	0.0793237	+	0.339022i
$503$	−9.97588			−0.444803			−0.222401	−	0.974955i	$-0.571390\pi$
$503$	−9.97588			−0.444803			−0.222401	+	0.974955i	$0.571390\pi$
$504$		0			0
$505$	15.5196			0.690612
$506$	−2.89903	−	12.3902i	−0.128878	−	0.550811i
$507$		0			0
$508$	2.47350	+	4.99639i	0.109744	+	0.221679i
$509$	−7.82922	−	13.5606i	−0.347024	−	0.601063i	0.638695	−	0.769460i	$-0.279474\pi$
$509$	−7.82922	−	13.5606i	−0.347024	−	0.601063i	−0.985719	+	0.168396i	$0.946141\pi$
$510$		0			0
$511$	26.2460	+	15.1532i	1.16106	+	0.670336i
$512$	10.8043	+	19.8813i	0.477486	+	0.878640i
$513$		0			0
$514$	20.1511	−	18.9026i	0.888826	−	0.833759i
$515$	−6.19601	−	3.57727i	−0.273029	−	0.157633i
$516$		0			0
$517$	3.59375	−	2.07485i	0.158053	−	0.0912519i
$518$	−5.22053	+	17.2575i	−0.229377	+	0.758251i
$519$		0			0
$520$	−9.62942	+	1.61264i	−0.422278	+	0.0707189i
$521$		−	9.78813i		−	0.428826i	−0.976743	−	0.214413i	$-0.931216\pi$
$521$		−	9.78813i		−	0.428826i	0.976743	−	0.214413i	$-0.0687838\pi$
$522$		0			0
$523$	−32.9015			−1.43868			−0.719342	−	0.694656i	$-0.755557\pi$
$523$	−32.9015			−1.43868			−0.719342	+	0.694656i	$0.755557\pi$
$524$	16.7088	−	25.0899i	0.729928	−	1.09606i
$525$		0			0
$526$	−4.60732	+	15.2304i	−0.200889	+	0.664079i
$527$	−4.02989	−	6.97997i	−0.175545	−	0.304052i
$528$		0			0
$529$	−18.2896	+	31.6786i	−0.795201	+	1.37733i
$530$	12.3352	+	13.1499i	0.535806	+	0.571194i
$531$		0			0
$532$	29.3140	+	1.87609i	1.27092	+	0.0813389i
$533$	−7.46391	+	12.9279i	−0.323298	+	0.559968i
$534$		0			0
$535$	−10.2282	+	5.90525i	−0.442203	+	0.255306i
$536$	29.5811	+	11.0558i	1.27771	+	0.477536i
$537$		0			0
$538$	19.4986	−	4.56225i	0.840646	−	0.196692i
$539$		−	13.2908i		−	0.572476i
$540$		0			0
$541$		−	26.4228i		−	1.13601i	−0.823027	−	0.568003i	$-0.807716\pi$
$541$		−	26.4228i		−	1.13601i	0.823027	−	0.568003i	$-0.192284\pi$
$542$	1.26162	+	5.39206i	0.0541913	+	0.231609i
$543$		0			0
$544$	7.72446	+	3.46419i	0.331183	+	0.148526i
$545$	−9.47149	+	5.46837i	−0.405714	+	0.234239i
$546$		0			0
$547$	17.7776	−	30.7917i	0.760116	−	1.31656i	−0.182674	−	0.983174i	$-0.558475\pi$
$547$	17.7776	−	30.7917i	0.760116	−	1.31656i	0.942790	−	0.333387i	$-0.108191\pi$
$548$	−17.4052	−	1.11393i	−0.743515	−	0.0475849i
$549$		0			0
$550$	4.47547	−	4.19820i	0.190835	−	0.179012i
$551$	2.42944	−	4.20792i	0.103498	−	0.179263i
$552$		0			0
$553$	−5.57242	−	9.65172i	−0.236964	−	0.410433i
$554$	35.8775	+	10.8532i	1.52429	+	0.461109i
$555$		0			0
$556$	3.95842	+	2.63614i	0.167874	+	0.111797i
$557$	18.4413			0.781384			0.390692	−	0.920522i	$-0.372236\pi$
$557$	18.4413			0.781384			0.390692	+	0.920522i	$0.372236\pi$
$558$		0			0
$559$		−	10.6450i		−	0.450236i
$560$	15.4240	+	11.7601i	0.651783	+	0.496955i
$561$		0			0
$562$	−1.44326	−	0.436597i	−0.0608803	−	0.0184168i
$563$	−35.4943	+	20.4926i	−1.49591	+	0.863661i	−0.999989	−	0.00470871i	$-0.998501\pi$
$563$	−35.4943	+	20.4926i	−1.49591	+	0.863661i	−0.495917	+	0.868370i	$0.665168\pi$
$564$		0			0
$565$	8.08387	+	4.66722i	0.340091	+	0.196352i
$566$	−3.44134	−	3.66862i	−0.144650	−	0.154204i
$567$		0			0
$568$	−5.56375	+	4.58756i	−0.233450	+	0.192490i
$569$	3.72340	+	2.14971i	0.156093	+	0.0901205i	0.576012	−	0.817441i	$-0.304608\pi$
$569$	3.72340	+	2.14971i	0.156093	+	0.0901205i	−0.419919	+	0.907562i	$0.637941\pi$
$570$		0			0
$571$	−2.17462	−	3.76656i	−0.0910052	−	0.157626i	0.816929	−	0.576738i	$-0.195675\pi$
$571$	−2.17462	−	3.76656i	−0.0910052	−	0.157626i	−0.907934	+	0.419112i	$0.862341\pi$
$572$	6.38056	−	3.15875i	0.266785	−	0.132074i
$573$		0			0
$574$	28.8752	−	6.75616i	1.20523	−	0.281997i
$575$	−28.7312			−1.19817
$576$		0			0
$577$	12.5475			0.522361			0.261180	−	0.965290i	$-0.415888\pi$
$577$	12.5475			0.522361			0.261180	+	0.965290i	$0.415888\pi$
$578$	−20.3254	+	4.75569i	−0.845424	+	0.197810i
$579$		0			0
$580$	2.87531	−	1.42345i	0.119391	−	0.0591054i
$581$	−9.86905	−	17.0937i	−0.409437	−	0.709166i
$582$		0			0
$583$	−11.3861	−	6.57376i	−0.471563	−	0.272257i
$584$	15.4175	−	12.7124i	0.637979	−	0.526042i
$585$		0			0
$586$	−15.0734	−	16.0690i	−0.622678	−	0.663803i
$587$	8.02388	+	4.63259i	0.331181	+	0.191207i	0.656365	−	0.754443i	$-0.272093\pi$
$587$	8.02388	+	4.63259i	0.331181	+	0.191207i	−0.325184	+	0.945651i	$0.605426\pi$
$588$		0			0
$589$	−15.9688	+	9.21958i	−0.657982	+	0.379886i
$590$	−13.2677	−	4.01358i	−0.546222	−	0.165236i
$591$		0			0
$592$	9.45362	+	7.20796i	0.388542	+	0.296245i
$593$		−	11.1342i		−	0.457228i	−0.973517	−	0.228614i	$-0.926581\pi$
$593$		−	11.1342i		−	0.457228i	0.973517	−	0.228614i	$-0.0734193\pi$
$594$		0			0
$595$	7.25666			0.297494
$596$	−29.7780	−	19.8309i	−1.21976	−	0.812305i
$597$		0			0
$598$	−31.9071	−	9.65214i	−1.30478	−	0.394705i
$599$	−22.8693	−	39.6108i	−0.934415	−	1.61845i	−0.775675	−	0.631133i	$-0.782590\pi$
$599$	−22.8693	−	39.6108i	−0.934415	−	1.61845i	−0.158740	−	0.987320i	$-0.550743\pi$
$600$		0			0
$601$	−11.2521	+	19.4892i	−0.458982	+	0.794980i	−0.998907	−	0.0467325i	$-0.985119\pi$
$601$	−11.2521	+	19.4892i	−0.458982	+	0.794980i	0.539925	+	0.841713i	$0.318453\pi$
$602$	−15.4233	+	14.4678i	−0.628608	+	0.589663i
$603$		0			0
$604$	−5.51192	−	0.352763i	−0.224277	−	0.0143537i
$605$	−5.44905	+	9.43803i	−0.221535	+	0.383710i
$606$		0			0
$607$	−24.7306	+	14.2782i	−1.00378	+	0.579535i	−0.909366	−	0.415997i	$-0.863433\pi$
$607$	−24.7306	+	14.2782i	−1.00378	+	0.579535i	−0.0944185	+	0.995533i	$0.530099\pi$
$608$	7.92538	−	17.6720i	0.321417	−	0.716695i
$609$		0			0
$610$	1.32915	+	5.68066i	0.0538157	+	0.230003i
$611$		−	10.8709i		−	0.439791i
$612$		0			0
$613$		−	40.4574i		−	1.63406i	−0.576596	−	0.817030i	$-0.695619\pi$
$613$		−	40.4574i		−	1.63406i	0.576596	−	0.817030i	$-0.304381\pi$
$614$	1.32289	−	0.309527i	0.0533876	−	0.0124915i
$615$		0			0
$616$	−13.2486	−	4.95156i	−0.533800	−	0.199504i
$617$	31.6715	−	18.2855i	1.27505	−	0.736148i	0.299112	−	0.954218i	$-0.403309\pi$
$617$	31.6715	−	18.2855i	1.27505	−	0.736148i	0.975933	+	0.218070i	$0.0699761\pi$
$618$		0			0
$619$	20.3697	−	35.2814i	0.818727	−	1.41808i	−0.0878927	−	0.996130i	$-0.528013\pi$
$619$	20.3697	−	35.2814i	0.818727	−	1.41808i	0.906620	−	0.421948i	$-0.138653\pi$
$620$	−12.1507	−	0.777643i	−0.487983	−	0.0312309i
$621$		0			0
$622$	−8.69892	−	9.27345i	−0.348795	−	0.371831i
$623$	−18.5273	+	32.0902i	−0.742279	+	1.28567i
$624$		0			0
$625$	−3.73321	−	6.46610i	−0.149328	−	0.258644i
$626$	−7.00943	+	23.1711i	−0.280153	+	0.926103i
$627$		0			0
$628$	−2.83087	+	4.25083i	−0.112964	+	0.169627i
$629$	4.44772			0.177342
$630$		0			0
$631$			15.0916i			0.600788i	0.953815	+	0.300394i	$0.0971182\pi$
$631$			15.0916i			0.600788i	−0.953815	+	0.300394i	$0.902882\pi$
$632$	−7.24746	+	1.21373i	−0.288289	+	0.0482797i
$633$		0			0
$634$	3.24744	−	10.7351i	0.128972	−	0.426344i
$635$	2.72884	−	1.57550i	0.108291	−	0.0625218i
$636$		0			0
$637$	−30.1531	−	17.4089i	−1.19471	−	0.689765i
$638$	−1.70634	+	1.60062i	−0.0675546	+	0.0633693i
$639$		0			0
$640$	10.8237	−	6.81165i	0.427846	−	0.269254i
$641$	26.9377	+	15.5525i	1.06398	+	0.614287i	0.926529	−	0.376222i	$-0.122777\pi$
$641$	26.9377	+	15.5525i	1.06398	+	0.614287i	0.137447	+	0.990509i	$0.456110\pi$
$642$		0			0
$643$	−1.93125	−	3.34503i	−0.0761612	−	0.131915i	0.825429	−	0.564505i	$-0.190933\pi$
$643$	−1.93125	−	3.34503i	−0.0761612	−	0.131915i	−0.901591	+	0.432590i	$0.857600\pi$
$644$	29.3806	+	59.3479i	1.15776	+	2.33863i
$645$		0			0
$646$	−1.65085	−	7.05560i	−0.0649520	−	0.277599i
$647$	24.1359			0.948879			0.474440	−	0.880288i	$-0.342651\pi$
$647$	24.1359			0.948879			0.474440	+	0.880288i	$0.342651\pi$
$648$		0			0
$649$	10.1079			0.396770
$650$	−3.66235	−	15.6526i	−0.143649	−	0.613944i
$651$		0			0
$652$	12.4276	−	6.15237i	0.486702	−	0.240945i
$653$	−16.2083	−	28.0736i	−0.634279	−	1.09860i	−0.986667	−	0.162750i	$-0.947964\pi$
$653$	−16.2083	−	28.0736i	−0.634279	−	1.09860i	0.352388	−	0.935854i	$-0.385370\pi$
$654$		0			0
$655$	−14.7547	−	8.51864i	−0.576515	−	0.332851i
$656$	2.49259	−	19.3937i	0.0973195	−	0.757195i
$657$		0			0
$658$	−15.7507	+	14.7748i	−0.614025	+	0.575984i
$659$	−19.7202	−	11.3855i	−0.768191	−	0.443515i	0.0640377	−	0.997947i	$-0.479602\pi$
$659$	−19.7202	−	11.3855i	−0.768191	−	0.443515i	−0.832229	+	0.554432i	$0.812936\pi$
$660$		0			0
$661$	−25.6004	+	14.7804i	−0.995740	+	0.574891i	−0.906985	−	0.421163i	$-0.861622\pi$
$661$	−25.6004	+	14.7804i	−0.995740	+	0.574891i	−0.0887549	+	0.996053i	$0.528289\pi$
$662$	−3.91752	+	12.9502i	−0.152259	+	0.503322i
$663$		0			0
$664$	−12.8356	+	2.14958i	−0.498119	+	0.0834200i
$665$		−	16.6018i		−	0.643790i
$666$		0			0
$667$	10.9542			0.424147
$668$	27.8605	+	18.5539i	1.07795	+	0.717872i
$669$		0			0
$670$	5.16800	−	17.0839i	0.199657	−	0.660007i
$671$	−2.12713	−	3.68430i	−0.0821171	−	0.142231i
$672$		0			0
$673$	8.89907	−	15.4136i	0.343034	−	0.594152i	−0.641961	−	0.766738i	$-0.721879\pi$
$673$	8.89907	−	15.4136i	0.343034	−	0.594152i	0.984995	+	0.172585i	$0.0552121\pi$
$674$	−33.0369	−	35.2188i	−1.27253	−	1.35658i
$675$		0			0
$676$	−0.469360	+	7.33376i	−0.0180523	+	0.282068i
$677$	22.9383	−	39.7303i	0.881591	−	1.52696i	0.0320192	−	0.999487i	$-0.489806\pi$
$677$	22.9383	−	39.7303i	0.881591	−	1.52696i	0.849572	−	0.527473i	$-0.176860\pi$
$678$		0			0
$679$	−24.9550	+	14.4078i	−0.957684	+	0.552919i
$680$	1.67508	−	4.48191i	0.0642365	−	0.171873i
$681$		0			0
$682$	8.64502	−	2.02274i	0.331035	−	0.0774548i
$683$		−	2.20513i		−	0.0843769i	−0.999110	−	0.0421884i	$-0.986567\pi$
$683$		−	2.20513i		−	0.0843769i	0.999110	−	0.0421884i	$-0.0134330\pi$
$684$		0			0
$685$			9.85735i			0.376630i
$686$	6.08336	+	25.9997i	0.232264	+	0.992675i
$687$		0			0
$688$	5.37546	+	12.8655i	0.204938	+	0.490493i
$689$	−29.8280	+	17.2212i	−1.13636	+	0.656075i
$690$		0			0
$691$	−10.2512	+	17.7556i	−0.389975	+	0.675457i	−0.992446	−	0.122684i	$-0.960850\pi$
$691$	−10.2512	+	17.7556i	−0.389975	+	0.675457i	0.602471	+	0.798141i	$0.294183\pi$
$692$	2.61073	−	40.7926i	0.0992449	−	1.55070i
$693$		0			0
$694$	24.9433	−	23.3980i	0.946835	−	0.888175i
$695$	1.34398	−	2.32784i	0.0509801	−	0.0883001i
$696$		0			0
$697$	−3.65776	−	6.33542i	−0.138547	−	0.239971i
$698$	−15.1903	−	4.59519i	−0.574963	−	0.173931i
$699$		0			0
$700$	−17.7011	+	26.5799i	−0.669039	+	1.00463i
$701$	−26.6854			−1.00789			−0.503947	−	0.863734i	$-0.668119\pi$
$701$	−26.6854			−1.00789			−0.503947	+	0.863734i	$0.668119\pi$
$702$		0			0
$703$		−	10.1755i		−	0.383776i
$704$	−6.11643	+	7.03968i	−0.230522	+	0.265318i
$705$		0			0
$706$	−9.14655	−	2.76690i	−0.344235	−	0.104134i
$707$	51.0052	−	29.4479i	1.91825	−	1.10750i
$708$		0			0
$709$	−37.8684	−	21.8633i	−1.42218	−	0.821095i	−0.425693	−	0.904868i	$-0.639970\pi$
$709$	−37.8684	−	21.8633i	−1.42218	−	0.821095i	−0.996485	+	0.0837727i	$0.973303\pi$
$710$	2.78838	+	2.97254i	0.104646	+	0.111558i
$711$		0			0
$712$	15.5430	+	18.8504i	0.582500	+	0.706450i
$713$	−36.0009	−	20.7851i	−1.34825	−	0.778410i
$714$		0			0
$715$	−2.01197	−	3.48483i	−0.0752433	−	0.130325i
$716$	3.62016	+	7.31260i	0.135292	+	0.273285i
$717$		0			0
$718$	28.0080	−	6.55324i	1.04525	−	0.244565i
$719$	13.9253			0.519327			0.259663	−	0.965699i	$-0.416388\pi$
$719$	13.9253			0.519327			0.259663	+	0.965699i	$0.416388\pi$
$720$		0			0
$721$	−27.1510			−1.01115
$722$	10.0216	−	2.34484i	0.372966	−	0.0872658i
$723$		0			0
$724$	−19.8076	−	40.0107i	−0.736145	−	1.48699i
$725$	2.64124	+	4.57475i	0.0980930	+	0.169902i
$726$		0			0
$727$	30.9380	+	17.8621i	1.14743	+	0.662468i	0.948259	−	0.317497i	$-0.102842\pi$
$727$	30.9380	+	17.8621i	1.14743	+	0.662468i	0.199169	+	0.979965i	$0.436176\pi$
$728$	−28.5872	+	23.5714i	−1.05951	+	0.873616i
$729$		0			0
$730$	−7.72676	−	8.23708i	−0.285980	−	0.304868i
$731$	4.51778	+	2.60834i	0.167096	+	0.0964730i
$732$		0			0
$733$	30.2141	−	17.4441i	1.11598	−	0.644312i	0.175610	−	0.984460i	$-0.443810\pi$
$733$	30.2141	−	17.4441i	1.11598	−	0.644312i	0.940372	+	0.340148i	$0.110477\pi$
$734$	−18.3185	−	5.54148i	−0.676148	−	0.204540i
$735$		0			0
$736$	43.4369	−	4.44676i	1.60110	−	0.163910i
$737$			13.0152i			0.479422i
$738$		0			0
$739$	13.1128			0.482361			0.241181	−	0.970480i	$-0.422465\pi$
$739$	13.1128			0.482361			0.241181	+	0.970480i	$0.422465\pi$
$740$	3.72427	−	5.59236i	0.136907	−	0.205579i
$741$		0			0
$742$	65.4911	+	19.8115i	2.40425	+	0.727305i
$743$	11.1665	+	19.3410i	0.409660	+	0.709551i	0.994851	−	0.101344i	$-0.0323142\pi$
$743$	11.1665	+	19.3410i	0.409660	+	0.709551i	−0.585192	+	0.810895i	$0.698981\pi$
$744$		0			0
$745$	−10.1104	+	17.5117i	−0.370415	+	0.641578i
$746$	−27.4365	+	25.7367i	−1.00452	+	0.942286i
$747$		0			0
$748$	−0.222843	+	3.48192i	−0.00814794	+	0.127312i
$749$	−22.4100	+	38.8153i	−0.818844	+	1.41828i
$750$		0			0
$751$	−6.99545	+	4.03882i	−0.255267	+	0.147379i	−0.622174	−	0.782879i	$-0.713750\pi$
$751$	−6.99545	+	4.03882i	−0.255267	+	0.147379i	0.366906	+	0.930258i	$0.380417\pi$
$752$	5.48955	+	13.1386i	0.200183	+	0.479114i
$753$		0			0
$754$	1.39632	+	5.96776i	0.0508511	+	0.217333i
$755$			3.12165i			0.113608i
$756$		0			0
$757$			12.7751i			0.464319i	0.972678	+	0.232160i	$0.0745792\pi$
$757$			12.7751i			0.464319i	−0.972678	+	0.232160i	$0.925421\pi$
$758$	39.2493	−	9.18346i	1.42560	−	0.333558i
$759$		0			0
$760$	−10.2537	−	3.83226i	−0.371941	−	0.139011i
$761$	−43.2325	+	24.9603i	−1.56718	+	0.904809i	−0.570679	+	0.821173i	$0.693320\pi$
$761$	−43.2325	+	24.9603i	−1.56718	+	0.904809i	−0.996496	+	0.0836361i	$0.973347\pi$
$762$		0			0
$763$	−20.7521	+	35.9437i	−0.751276	+	1.30125i
$764$	1.85855	−	29.0398i	0.0672399	−	1.05062i
$765$		0			0
$766$	−19.4504	−	20.7350i	−0.702771	−	0.749186i
$767$	13.2398	−	22.9320i	0.478060	−	0.828025i
$768$		0			0
$769$	−14.2517	−	24.6846i	−0.513929	−	0.890150i	−0.999869	−	0.0161588i	$-0.994856\pi$
$769$	−14.2517	−	24.6846i	−0.513929	−	0.890150i	0.485941	−	0.873992i	$-0.338477\pi$
$770$	−2.31460	+	7.65138i	−0.0834124	+	0.275737i
$771$		0			0
$772$	7.30866	+	4.86726i	0.263044	+	0.175176i
$773$	20.8254			0.749037			0.374518	−	0.927220i	$-0.377808\pi$
$773$	20.8254			0.749037			0.374518	+	0.927220i	$0.377808\pi$
$774$		0			0
$775$		−	20.0466i		−	0.720096i
$776$	3.13817	+	18.7387i	0.112654	+	0.672679i
$777$		0			0
$778$	−0.885390	+	2.92684i	−0.0317428	+	0.104932i
$779$	−14.4942	+	8.36822i	−0.519308	+	0.299822i
$780$		0			0
$781$	−2.57384	−	1.48601i	−0.0920991	−	0.0531735i
$782$	11.9146	−	11.1764i	0.426065	−	0.399668i
$783$		0			0
$784$	45.2339	+	5.81375i	1.61550	+	0.207634i
$785$	2.49980	+	1.44326i	0.0892218	+	0.0515122i
$786$		0			0
$787$	10.4386	+	18.0802i	0.372096	+	0.644488i	0.989888	−	0.141853i	$-0.0453060\pi$
$787$	10.4386	+	18.0802i	0.372096	+	0.644488i	−0.617792	+	0.786341i	$0.711973\pi$
$788$	−13.7964	+	6.82999i	−0.491475	+	0.243308i
$789$		0			0
$790$	0.946206	+	4.04400i	0.0336645	+	0.143879i
$791$	35.4236			1.25952
$792$		0			0
$793$	−11.1448			−0.395765
$794$	−6.07347	−	25.9575i	−0.215540	−	0.921197i
$795$		0			0
$796$	18.6154	+	37.6024i	0.659804	+	1.33278i
$797$	−14.4238	−	24.9828i	−0.510918	−	0.884935i	−0.999920	−	0.0126529i	$-0.995972\pi$
$797$	−14.4238	−	24.9828i	−0.510918	−	0.884935i	0.489002	−	0.872283i	$-0.337361\pi$
$798$		0			0
$799$	4.61367	+	2.66370i	0.163220	+	0.0942350i
$800$	12.3305	+	17.0682i	0.435948	+	0.603453i
$801$		0			0
$802$	−17.9446	+	16.8329i	−0.633647	+	0.594390i
$803$	7.13225	+	4.11780i	0.251691	+	0.145314i
$804$		0			0
$805$	32.4136	−	18.7140i	1.14243	−	0.659582i
$806$	6.73460	−	22.2626i	0.237216	−	0.784165i
$807$		0			0
$808$	−6.41406	−	38.2997i	−0.225646	−	1.34738i
$809$			43.6746i			1.53552i	0.640739	+	0.767759i	$0.278628\pi$
$809$			43.6746i			1.53552i	−0.640739	+	0.767759i	$0.721372\pi$
$810$		0			0
$811$	42.3445			1.48692			0.743458	−	0.668782i	$-0.233184\pi$
$811$	42.3445			1.48692			0.743458	+	0.668782i	$0.233184\pi$
$812$	6.74880	−	10.1340i	0.236836	−	0.355633i
$813$		0			0
$814$	−1.41866	+	4.68965i	−0.0497239	+	0.164372i
$815$	−3.91876	−	6.78749i	−0.137268	−	0.237755i
$816$		0			0
$817$	5.96737	−	10.3358i	0.208772	−	0.361603i
$818$	19.9064	+	21.2212i	0.696012	+	0.741981i
$819$		0			0
$820$	−11.0287	−	0.705833i	−0.385137	−	0.0246488i
$821$	−1.40953	+	2.44138i	−0.0491930	+	0.0852047i	−0.889573	−	0.456792i	$-0.848998\pi$
$821$	−1.40953	+	2.44138i	−0.0491930	+	0.0852047i	0.840380	+	0.541997i	$0.182332\pi$
$822$		0			0
$823$	−4.46763	+	2.57939i	−0.155732	+	0.0899118i	−0.575841	−	0.817562i	$-0.695325\pi$
$823$	−4.46763	+	2.57939i	−0.155732	+	0.0899118i	0.420109	+	0.907474i	$0.361992\pi$
$824$	−6.26736	+	16.7692i	−0.218334	+	0.584181i
$825$		0			0
$826$	−51.2200	+	11.9843i	−1.78217	+	0.416989i
$827$		−	21.8630i		−	0.760251i	−0.924935	−	0.380125i	$-0.875881\pi$
$827$		−	21.8630i		−	0.760251i	0.924935	−	0.380125i	$-0.124119\pi$
$828$		0			0
$829$			22.0815i			0.766924i	0.923557	+	0.383462i	$0.125268\pi$
$829$			22.0815i			0.766924i	−0.923557	+	0.383462i	$0.874732\pi$
$830$	1.67578	+	7.16213i	0.0581672	+	0.248601i
$831$		0			0
$832$	7.95945	+	23.0973i	0.275944	+	0.800756i
$833$	14.7768	−	8.53139i	0.511986	−	0.295595i
$834$		0			0
$835$	9.45931	−	16.3840i	0.327353	−	0.566992i
$836$	7.96594	+	0.509820i	0.275508	+	0.0176325i
$837$		0			0
$838$	−28.8174	+	27.0321i	−0.995482	+	0.933808i
$839$	−25.4035	+	44.0002i	−0.877026	+	1.51905i	−0.0224378	+	0.999748i	$0.507143\pi$
$839$	−25.4035	+	44.0002i	−0.877026	+	1.51905i	−0.854588	+	0.519306i	$0.826191\pi$
$840$		0			0
$841$	13.4930	+	23.3705i	0.465276	+	0.805881i
$842$	−9.81317	−	2.96856i	−0.338184	−	0.102303i
$843$		0			0
$844$	7.93976	+	5.28754i	0.273298	+	0.182005i
$845$	4.15343			0.142882
$846$		0			0
$847$			41.3575i			1.42106i
$848$	27.3537	−	35.8759i	0.939330	−	1.23198i
$849$		0			0
$850$	7.54039	+	2.28103i	0.258633	+	0.0782386i
$851$	19.8668	−	11.4701i	0.681026	−	0.393191i
$852$		0			0
$853$	45.4891	+	26.2631i	1.55752	+	0.899233i	0.997494	+	0.0707558i	$0.0225411\pi$
$853$	45.4891	+	26.2631i	1.55752	+	0.899233i	0.560023	+	0.828477i	$0.310792\pi$
$854$	15.1471	+	16.1475i	0.518324	+	0.552557i
$855$		0			0
$856$	18.8004	+	22.8009i	0.642583	+	0.779319i
$857$	48.4564	+	27.9763i	1.65524	+	0.955653i	0.974867	+	0.222786i	$0.0715151\pi$
$857$	48.4564	+	27.9763i	1.65524	+	0.955653i	0.680372	+	0.732867i	$0.261818\pi$
$858$		0			0
$859$	15.4078	+	26.6871i	0.525708	+	0.910554i	0.999552	+	0.0299443i	$0.00953300\pi$
$859$	15.4078	+	26.6871i	0.525708	+	0.910554i	−0.473843	+	0.880609i	$0.657134\pi$
$860$	7.06254	−	3.49636i	0.240831	−	0.119225i
$861$		0			0
$862$	−51.9143	+	12.1468i	−1.76821	+	0.413721i
$863$	25.1750			0.856966			0.428483	−	0.903550i	$-0.359048\pi$
$863$	25.1750			0.856966			0.428483	+	0.903550i	$0.359048\pi$
$864$		0			0
$865$	−23.1027			−0.785514
$866$	−49.7360	+	11.6371i	−1.69010	+	0.395446i
$867$		0			0
$868$	−41.4088	+	20.4998i	−1.40551	+	0.695808i
$869$	−1.51428	−	2.62281i	−0.0513685	−	0.0889728i
$870$		0			0
$871$	29.5278	+	17.0479i	1.00051	+	0.577646i
$872$	17.4095	+	21.1141i	0.589560	+	0.715012i
$873$		0			0
$874$	−25.5694	−	27.2582i	−0.864899	−	0.922022i
$875$	36.6276	+	21.1470i	1.23824	+	0.714898i
$876$		0			0
$877$	31.8486	−	18.3878i	1.07545	−	0.620913i	0.145786	−	0.989316i	$-0.453429\pi$
$877$	31.8486	−	18.3878i	1.07545	−	0.620913i	0.929666	+	0.368404i	$0.120096\pi$
$878$	14.1024	+	4.26607i	0.475932	+	0.143973i
$879$		0			0
$880$	4.19141	+	3.19576i	0.141292	+	0.107729i
$881$			8.15439i			0.274728i	0.990521	+	0.137364i	$0.0438631\pi$
$881$			8.15439i			0.274728i	−0.990521	+	0.137364i	$0.956137\pi$
$882$		0			0
$883$	−20.3792			−0.685814			−0.342907	−	0.939369i	$-0.611412\pi$
$883$	−20.3792			−0.685814			−0.342907	+	0.939369i	$0.611412\pi$
$884$	7.60760	+	5.06634i	0.255871	+	0.170399i
$885$		0			0
$886$	−48.1268	−	14.5587i	−1.61685	−	0.489110i
$887$	22.3561	+	38.7220i	0.750646	+	1.30016i	0.947510	+	0.319726i	$0.103591\pi$
$887$	22.3561	+	38.7220i	0.750646	+	1.30016i	−0.196864	+	0.980431i	$0.563076\pi$
$888$		0			0
$889$	5.97891	−	10.3558i	0.200526	−	0.347322i
$890$	10.0712	−	9.44726i	0.337588	−	0.316673i
$891$		0			0
$892$	−28.8713	−	1.84776i	−0.966684	−	0.0618677i
$893$	6.09402	−	10.5551i	0.203928	−	0.353214i
$894$		0			0
$895$	3.99387	−	2.30586i	0.133500	−	0.0770765i
$896$	22.6474	−	42.9242i	0.756597	−	1.43400i
$897$		0			0
$898$	−5.40479	−	23.0996i	−0.180360	−	0.770843i
$899$			7.64305i			0.254910i
$900$		0			0
$901$		−	16.8788i		−	0.562315i
$902$	7.84671	−	1.83596i	0.261267	−	0.0611307i
$903$		0			0
$904$	8.17697	−	21.8786i	0.271962	−	0.727670i
$905$	−21.8524	+	12.6165i	−0.726398	+	0.419386i
$906$		0			0
$907$	7.99519	−	13.8481i	0.265476	−	0.459818i	−0.702212	−	0.711968i	$-0.747804\pi$
$907$	7.99519	−	13.8481i	0.265476	−	0.459818i	0.967688	+	0.252150i	$0.0811376\pi$
$908$	−1.29482	−	0.0828684i	−0.0429701	−	0.00275009i
$909$		0			0
$910$	14.3270	+	15.2733i	0.474937	+	0.506304i
$911$	14.1609	−	24.5275i	0.469173	−	0.812631i	−0.530206	−	0.847869i	$-0.677885\pi$
$911$	14.1609	−	24.5275i	0.469173	−	0.812631i	0.999379	+	0.0352377i	$0.0112188\pi$
$912$		0			0
$913$	−2.68187	−	4.64514i	−0.0887570	−	0.153732i
$914$	0.556437	−	1.83941i	0.0184053	−	0.0608424i
$915$		0			0
$916$	−15.3619	+	23.0674i	−0.507573	+	0.762170i
$917$	−64.6553			−2.13511
$918$		0			0
$919$			17.1474i			0.565642i	0.959173	+	0.282821i	$0.0912702\pi$
$919$			17.1474i			0.565642i	−0.959173	+	0.282821i	$0.908730\pi$
$920$	−4.07611	−	24.3393i	−0.134385	−	0.802444i
$921$		0			0
$922$	4.15553	−	13.7369i	0.136855	−	0.452402i
$923$	−6.74265	+	3.89287i	−0.221937	+	0.128135i
$924$		0			0
$925$	9.58047	+	5.53129i	0.315004	+	0.181868i
$926$	−27.7094	+	25.9927i	−0.910589	+	0.854174i
$927$		0			0
$928$	−4.70116	−	6.50750i	−0.154323	−	0.213619i
$929$	−38.0670	−	21.9780i	−1.24894	−	0.721075i	−0.278040	−	0.960569i	$-0.589685\pi$
$929$	−38.0670	−	21.9780i	−1.24894	−	0.721075i	−0.970898	+	0.239495i	$0.923018\pi$
$930$		0			0
$931$	−19.5181	−	33.8064i	−0.639680	−	1.10796i
$932$	−20.5219	−	41.4535i	−0.672216	−	1.35785i
$933$		0			0
$934$	−10.1207	−	43.2548i	−0.331158	−	1.41534i
$935$	1.97197			0.0644902
$936$		0			0
$937$	−13.5845			−0.443786			−0.221893	−	0.975071i	$-0.571223\pi$
$937$	−13.5845			−0.443786			−0.221893	+	0.975071i	$0.571223\pi$
$938$	−15.4314	−	65.9523i	−0.503852	−	2.15342i
$939$		0			0
$940$	7.21243	−	3.57057i	0.235244	−	0.116459i
$941$	13.5116	+	23.4028i	0.440466	+	0.762909i	0.997724	−	0.0674301i	$-0.0214800\pi$
$941$	13.5116	+	23.4028i	0.440466	+	0.762909i	−0.557258	+	0.830339i	$0.688147\pi$
$942$		0			0
$943$	−32.6765	−	18.8658i	−1.06409	−	0.614354i
$944$	−4.42146	+	34.4012i	−0.143906	+	1.11966i
$945$		0			0
$946$	−4.19122	+	3.93156i	−0.136268	+	0.127826i
$947$	−34.5376	−	19.9403i	−1.12232	−	0.647972i	−0.180328	−	0.983607i	$-0.557716\pi$
$947$	−34.5376	−	19.9403i	−1.12232	−	0.647972i	−0.941992	+	0.335634i	$0.891049\pi$
$948$		0			0
$949$	18.6843	−	10.7874i	0.606516	−	0.350172i
$950$	5.21853	−	17.2509i	0.169312	−	0.559694i
$951$		0			0
$952$	−2.99909	−	17.9082i	−0.0972011	−	0.580409i
$953$		−	14.0999i		−	0.456741i	−0.973574	−	0.228371i	$-0.926660\pi$
$953$		−	14.0999i		−	0.456741i	0.973574	−	0.228371i	$-0.0733398\pi$
$954$		0			0
$955$	−16.4465			−0.532197
$956$	−24.7724	−	16.4974i	−0.801197	−	0.533563i
$957$		0			0
$958$	−1.98590	+	6.56479i	−0.0641615	+	0.212099i
$959$	18.7040	+	32.3963i	0.603983	+	1.04613i
$960$		0			0
$961$	−0.997565	+	1.72783i	−0.0321795	+	0.0557366i
$962$	8.78127	+	9.36124i	0.283120	+	0.301818i
$963$		0			0
$964$	−1.50210	+	23.4704i	−0.0483795	+	0.755930i
$965$	2.48147	−	4.29803i	0.0798813	−	0.138358i
$966$		0			0
$967$	45.4687	−	26.2514i	1.46217	−	0.844187i	0.463063	−	0.886326i	$-0.346750\pi$
$967$	45.4687	−	26.2514i	1.46217	−	0.844187i	0.999112	+	0.0421387i	$0.0134171\pi$
$968$	25.5435	+	9.54672i	0.821000	+	0.306843i
$969$		0			0
$970$	10.4560	−	2.44646i	0.335721	−	0.0785512i
$971$		−	61.3864i		−	1.96998i	−0.172599	−	0.984992i	$-0.555216\pi$
$971$		−	61.3864i		−	1.96998i	0.172599	−	0.984992i	$-0.444784\pi$
$972$		0			0
$973$		−	10.2006i		−	0.327017i
$974$	7.49625	+	32.0383i	0.240195	+	1.02657i
$975$		0			0
$976$	13.4696	−	5.62787i	0.431152	−	0.180144i
$977$	25.9568	−	14.9862i	0.830431	−	0.479450i	−0.0235691	−	0.999722i	$-0.507503\pi$
$977$	25.9568	−	14.9862i	0.830431	−	0.479450i	0.854000	+	0.520273i	$0.174170\pi$
$978$		0			0
$979$	−5.03471	+	8.72037i	−0.160910	+	0.278704i
$980$	1.64629	−	25.7233i	0.0525889	−	0.821702i
$981$		0			0
$982$	11.2924	−	10.5928i	0.360354	−	0.338029i
$983$	−21.1703	+	36.6681i	−0.675228	+	1.16953i	0.301174	+	0.953569i	$0.402622\pi$
$983$	−21.1703	+	36.6681i	−0.675228	+	1.16953i	−0.976402	+	0.215961i	$0.930712\pi$
$984$		0			0
$985$	4.35037	+	7.53506i	0.138614	+	0.240087i
$986$	−2.87488	−	0.869673i	−0.0915549	−	0.0276960i
$987$		0			0
$988$	11.5908	−	17.4047i	0.368752	−	0.553717i
$989$	26.9063			0.855572
$990$		0			0
$991$			12.3787i			0.393222i	0.980482	+	0.196611i	$0.0629937\pi$
$991$			12.3787i			0.393222i	−0.980482	+	0.196611i	$0.937006\pi$
$992$	3.10264	+	30.3073i	0.0985089	+	0.962256i
$993$		0			0
$994$	14.8043	+	4.47842i	0.469565	+	0.142047i
$995$	20.5370	−	11.8571i	0.651068	−	0.375894i
$996$		0			0
$997$	6.20535	+	3.58266i	0.196525	+	0.113464i	0.595034	−	0.803701i	$-0.297139\pi$
$997$	6.20535	+	3.58266i	0.196525	+	0.113464i	−0.398508	+	0.917165i	$0.630472\pi$
$998$	−37.6196	−	40.1042i	−1.19083	−	1.26948i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.l.b.35.1		16
3.2	odd	2		72.2.l.b.11.8	yes	16
4.3	odd	2		864.2.p.b.143.4		16
8.3	odd	2	inner	216.2.l.b.35.3		16
8.5	even	2		864.2.p.b.143.5		16
9.2	odd	6		648.2.f.b.323.5		16
9.4	even	3		72.2.l.b.59.6	yes	16
9.5	odd	6	inner	216.2.l.b.179.3		16
9.7	even	3		648.2.f.b.323.12		16
12.11	even	2		288.2.p.b.47.6		16
24.5	odd	2		288.2.p.b.47.5		16
24.11	even	2		72.2.l.b.11.6	✓	16
36.7	odd	6		2592.2.f.b.1295.9		16
36.11	even	6		2592.2.f.b.1295.7		16
36.23	even	6		864.2.p.b.719.5		16
36.31	odd	6		288.2.p.b.239.5		16
72.5	odd	6		864.2.p.b.719.4		16
72.11	even	6		648.2.f.b.323.11		16
72.13	even	6		288.2.p.b.239.6		16
72.29	odd	6		2592.2.f.b.1295.10		16
72.43	odd	6		648.2.f.b.323.6		16
72.59	even	6	inner	216.2.l.b.179.1		16
72.61	even	6		2592.2.f.b.1295.8		16
72.67	odd	6		72.2.l.b.59.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.6	✓	16	24.11	even	2
72.2.l.b.11.8	yes	16	3.2	odd	2
72.2.l.b.59.6	yes	16	9.4	even	3
72.2.l.b.59.8	yes	16	72.67	odd	6
216.2.l.b.35.1		16	1.1	even	1	trivial
216.2.l.b.35.3		16	8.3	odd	2	inner
216.2.l.b.179.1		16	72.59	even	6	inner
216.2.l.b.179.3		16	9.5	odd	6	inner
288.2.p.b.47.5		16	24.5	odd	2
288.2.p.b.47.6		16	12.11	even	2
288.2.p.b.239.5		16	36.31	odd	6
288.2.p.b.239.6		16	72.13	even	6
648.2.f.b.323.5		16	9.2	odd	6
648.2.f.b.323.6		16	72.43	odd	6
648.2.f.b.323.11		16	72.11	even	6
648.2.f.b.323.12		16	9.7	even	3
864.2.p.b.143.4		16	4.3	odd	2
864.2.p.b.143.5		16	8.5	even	2
864.2.p.b.719.4		16	72.5	odd	6
864.2.p.b.719.5		16	36.23	even	6
2592.2.f.b.1295.7		16	36.11	even	6
2592.2.f.b.1295.8		16	72.61	even	6
2592.2.f.b.1295.9		16	36.7	odd	6
2592.2.f.b.1295.10		16	72.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37702 + 0.322193i) q^{2} +(1.79238 - 0.887333i) q^{4} +(-0.565188 - 0.978934i) q^{5} +(-3.71499 - 2.14485i) q^{7} +(-2.18226 + 1.79937i) q^{8} +O(q^{10})\)	\(q+(-1.37702 + 0.322193i) q^{2} +(1.79238 - 0.887333i) q^{4} +(-0.565188 - 0.978934i) q^{5} +(-3.71499 - 2.14485i) q^{7} +(-2.18226 + 1.79937i) q^{8} +(1.09368 + 1.16591i) q^{10} +(-1.00953 - 0.582853i) q^{11} +(-2.64466 + 1.52689i) q^{13} +(5.80668 + 1.75656i) q^{14} +(2.42528 - 3.18088i) q^{16} -1.49654i q^{17} -3.42378 q^{19} +(-1.88167 - 1.25312i) q^{20} +(1.57794 + 0.477339i) q^{22} +(-3.85938 - 6.68464i) q^{23} +(1.86113 - 3.22356i) q^{25} +(3.14980 - 2.95466i) q^{26} +(-8.56188 - 0.547960i) q^{28} +(-0.709580 + 1.22903i) q^{29} +(4.66408 - 2.69281i) q^{31} +(-2.31481 + 5.16156i) q^{32} +(0.482173 + 2.06077i) q^{34} +4.84897i q^{35} +2.97201i q^{37} +(4.71462 - 1.10312i) q^{38} +(2.99485 + 1.11931i) q^{40} +(4.23339 - 2.44415i) q^{41} +(-1.74292 + 3.01882i) q^{43} +(-2.32665 - 0.148906i) q^{44} +(7.46820 + 7.96144i) q^{46} +(-1.77991 + 3.08289i) q^{47} +(5.70075 + 9.87399i) q^{49} +(-1.52420 + 5.03856i) q^{50} +(-3.38538 + 5.08347i) q^{52} +11.2786 q^{53} +1.31769i q^{55} +(11.9665 - 2.00402i) q^{56} +(0.581124 - 1.92102i) q^{58} +(-7.50935 + 4.33553i) q^{59} +(3.16057 + 1.82476i) q^{61} +(-5.55494 + 5.21079i) q^{62} +(1.52453 - 7.85340i) q^{64} +(2.98946 + 1.72596i) q^{65} +(-5.58255 - 9.66925i) q^{67} +(-1.32793 - 2.68237i) q^{68} +(-1.56230 - 6.67714i) q^{70} +2.54954 q^{71} -7.06491 q^{73} +(-0.957560 - 4.09253i) q^{74} +(-6.13672 + 3.03803i) q^{76} +(2.50026 + 4.33059i) q^{77} +(2.24998 + 1.29902i) q^{79} +(-4.48461 - 0.576391i) q^{80} +(-5.04198 + 4.72961i) q^{82} +(3.98482 + 2.30064i) q^{83} +(-1.46501 + 0.845824i) q^{85} +(1.42740 - 4.71855i) q^{86} +(3.25183 - 0.544584i) q^{88} -8.63803i q^{89} +13.0998 q^{91} +(-12.8490 - 8.55689i) q^{92} +(1.45769 - 4.81869i) q^{94} +(1.93508 + 3.35165i) q^{95} +(3.35869 - 5.81742i) q^{97} +(-11.0314 - 11.7600i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4	\( 16 q + 3 q^{2} - 5 q^{4} - 12 q^{11} + 18 q^{14} + 7 q^{16} - 4 q^{19} - 18 q^{20} - q^{22} - 14 q^{25} - 12 q^{28} - 27 q^{32} - 13 q^{34} + 15 q^{38} - 12 q^{40} + 36 q^{41} + 8 q^{43} + 12 q^{46} + 10 q^{49} - 51 q^{50} - 18 q^{52} + 66 q^{56} + 12 q^{58} - 12 q^{59} + 34 q^{64} + 6 q^{65} - 16 q^{67} + 9 q^{68} + 18 q^{70} - 4 q^{73} + 60 q^{74} - 7 q^{76} - 22 q^{82} - 54 q^{83} + 51 q^{86} - 13 q^{88} - 36 q^{91} - 84 q^{92} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 12 * q^11 + 18 * q^14 + 7 * q^16 - 4 * q^19 - 18 * q^20 - q^22 - 14 * q^25 - 12 * q^28 - 27 * q^32 - 13 * q^34 + 15 * q^38 - 12 * q^40 + 36 * q^41 + 8 * q^43 + 12 * q^46 + 10 * q^49 - 51 * q^50 - 18 * q^52 + 66 * q^56 + 12 * q^58 - 12 * q^59 + 34 * q^64 + 6 * q^65 - 16 * q^67 + 9 * q^68 + 18 * q^70 - 4 * q^73 + 60 * q^74 - 7 * q^76 - 22 * q^82 - 54 * q^83 + 51 * q^86 - 13 * q^88 - 36 * q^91 - 84 * q^92 + 24 * q^94 + 8 * q^97

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